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A110324 Inverse of a number triangle related to the Jacobsthal numbers. 3
1, -1, 1, -4, -2, 1, 0, -12, -3, 1, 0, 0, -24, -4, 1, 0, 0, 0, -40, -5, 1, 0, 0, 0, 0, -60, -6, 1, 0, 0, 0, 0, 0, -84, -7, 1, 0, 0, 0, 0, 0, 0, -112, -8, 1, 0, 0, 0, 0, 0, 0, 0, -144, -9, 1, 0, 0, 0, 0, 0, 0, 0, 0, -180, -10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -220, -11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -264, -12, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are A110325. Diagonal sums are A110326. Inverse of A110321. The result can be generalized as follows: The triangle whose columns have e.g.f. (x^k/k!)/(1-a*x-b*x^2) has inverse T(n,k)=if(n=k,1,if(n-k=1,-a*binomial(n,1),if(n-k=2,-2*b*binomial(n,2),0)))

LINKS

Table of n, a(n) for n=0..90.

FORMULA

T(n, k)=if(n=k, 1, if(n-k=1, -binomial(n, 1), if(n-k=2, -4*binomial(n, 2), 0)))

EXAMPLE

Rows begin

1;

-1,1;

-4,-2,1;

0,-12,-3,1;

0,0,-24,-4,1;

0,0,0,-40,-5,1;

0,0,0,0,-60,-6,1;

CROSSREFS

Sequence in context: A256702 A266921 A248721 * A266861 A265435 A277004

Adjacent sequences:  A110321 A110322 A110323 * A110325 A110326 A110327

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Jul 20 2005

STATUS

approved

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Last modified January 27 01:45 EST 2021. Contains 340443 sequences. (Running on oeis4.)